What are these handles?
These are so called "bones" they make up the "armature"
They are commonly used to control the mesh when animating.
Example: the bending of the fingers when doing a first is controlled by bones in real life, so is it in blender, but simpler.

In your case they control the animation of the pistol. Be it the magazine snapping out. The recoil. Or just the whole model when moving.

It's a large subject and you can watch many tutorials on youtube.